## Abstract

In this article, we discuss a least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition. Assuming that Ω and B are two bounded sub-domains of R^{d}, with B‾⊂Ω, in order to solve the incompressible Navier–Stokes equations with a Navier slip condition on the boundary γ of the obstacle B, we advocate a fictitious domain method where one solves a simpler variant of the original problem on the whole Ω, followed by a well-chosen correction over B. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. A detailed discussion of the finite element implementation of the above methodology is also provided. Numerical results are given; they suggest optimal order of convergence.

Original language | English |
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Pages (from-to) | 281-297 |

Number of pages | 17 |

Journal | Journal of Computational Physics |

Volume | 366 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

## Scopus Subject Areas

- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

## User-Defined Keywords

- Fictitious domain method
- Incompressible viscous flow
- Least-squares
- Navier slip boundary condition